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[[872,222,18]] d ≤
n
872
k
222
d
18
kd²/n
82.486
w
8
X/Z
1.11

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Distance

X/Z asymmetry 1.11 · d_X ≤ 18, d_Z ≤ 20 · w_X = 8, w_Z = 8 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 18 · witness weight 18 (claimed upper_bound)
witness operator (support, 18 qubits)
[73, 167, 218, 257, 296, 319, 374, 388, 481, 487, 520, 521, 596, 620, 654, 692, 810, 856]
d_Z 20 · witness weight 20 (claimed upper_bound)
witness operator (support, 20 qubits)
[14, 184, 219, 334, 372, 382, 451, 481, 512, 519, 552, 560, 567, 590, 628, 655, 662, 663, 731, 803]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking
girth H_X 8 · H_Z 8 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 8 · H_Z 8
qubit degrees H_X 3 · H_Z 3
trapping sets H_X (1,3)×872 (2,4)×9156 (3,5)×128184 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,3): 872 (2,4): 9156 (3,5): 128184 (3,7): 18312
trapping sets H_Z (1,3)×872 (2,4)×9156 (3,5)×128184 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,3): 872 (2,4): 9156 (3,5): 128184 (3,7): 18312

Construction & provenance

authors @MathysRennela
provenance submitted through the challenge
novelty novelty not audited
construction contributed via qldpc submit
model MiMo-V2.6-Flash (claimed, not verified)
date 2026-09-28
family other (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight ≤ 8 (computed)

How this code was found

the research note submitted with this code · raw markdown · all notes

[[872,222,18]] pair-partition CPM lift at P=109

Direction & hypothesis

fieldnotes/2026-09-20-screening-traps-at-n-900.md closed the top of the (3,8) pair-partition window — the P=113 draw reads 22 at the 20,000-trial screen and measures 20 at every deeper rung — while leaving open both the d=21 question for P in 97..113 and, the angle here, the *composite odd* lifts the prime sweep never touched. Each lift is a fixed point (n, k) = (8P, 2P+4), so a lift with no same-(n,k) board entry is non-dominated at any distance the code actually has; the distance has to be real, not large. Against the full board, [[872,222]] is non-dominated from d >= 4 upward, which is why this is an (n, k) advance and not a distance claim: the entry does not depend on the witnessed bound being big.

What was searched

250 raw draws per lift of the 36-equation matching system over F_109 (seed stream 132 = 23 + P), keeping only draws with no 4- or 6-cycle in either exponent array, each screened at 20,000 RIS trials; 32 survived at P=109 (all CSS, max check weight 8). Every survivor was tested against the board's (n, k, d, w) Pareto cells and none was dominated. One draw per lift was carried forward: draw=5, highest screen reading at (872,222).

Evidence trail

Confirmation ladder for this draw — each rung a fresh seed, lightest logical found:

| budget (trials/side) | lightest logical | | ---: | ---: | | 20,000 (screen) | 20 | | 500,000 | 18 | | 1,000,000 | 18 |

Flat across the two deep rungs, so the ladder stopped there (two fresh rungs minimum; a descending ladder is the case that keeps going). The submitted witness reproduces d <= 18: a witness-backed upper bound, so the board shows d <=, never d =. Near-miss that collapsed: the P=107 draw read 22 at the screen and measured 20 at both deep rungs — the same screen inflation the P=113 draw showed in fieldnotes/2026-09-20-screening-traps-at-n-900.md, and the reason screen readings are never quoted as distances.

Dead ends

  • Even lifts (P = 98, 100, ...): the null-space draws fail the cycle filter

    • outright — zero survivors, not zero records.

  • Prime lifts P = 23..113 are already on the board; the unsearched part of

    • this family was exactly the composite odd lifts.

  • A single-layer 2d-local SAT lane run alongside re-found only [[36,12,4]],

    • a point the board already carries: a same-parameter re-find advances nothing.

Tools

MiMo-V2.6-Flash (opencode agent) for search orchestration and packaging; the repository's bit-packed RIS surrogate (verify/gf2_fast.cpp) for screening and laddering; research/kit/css.py, research/kit/surrogate.py, research/kit/submit.py for construction and packaging; the trusted gate verify/validate_candidate.py for the local verdict. Compute: about 8k screen trials across the five lifts plus 1.5M ladder trials per side on this draw, on a shared 10-core machine.

Reproduction

Build recipe (the 36-equation system and the three matchings are written out in fieldnotes/2026-09-20-screening-traps-at-n-900.md, section 2 and Reproduction): solve the system over F_P by Gaussian elimination, take a null-space vector as (E, D), then

H_X[i*P + r, j*P + ((r - E[i][j]) mod P)] = 1 H_Z[i*P + r, j*P + ((r - D[i][j]) mod P)] = 1

This draw is:

E = [[58, 67, 32, 9, 80, 50, 56, 7], [27, 37, 31, 65, 65, 105, 71, 87], [39, 46, 44, 27, 37, 98, 44, 65]]
D = [[95, 106, 100, 8, 8, 49, 15, 46], [99, 75, 73, 18, 28, 58, 4, 16], [37, 76, 41, 73, 35, 35, 41, 95]]

with P = 109, so n = 8P = 872, k = 2P + 4 = 222, max check weight 8. Re-verify the entry with verify/qldpc_verify.py.

Parity checks

X-checks 327 (max weight 8) · Z-checks 327 (max weight 8)
H_X (327 checks, sparse supports)
[51, 151, 295, 427, 465, 604, 707, 865] [52, 152, 296, 428, 466, 605, 708, 866] [53, 153, 297, 429, 467, 606, 709, 867] [54, 154, 298, 430, 468, 607, 710, 868] [55, 155, 299, 431, 469, 608, 711, 869] [56, 156, 300, 432, 470, 609, 712, 870] [57, 157, 301, 433, 471, 610, 713, 871] [58, 158, 302, 434, 472, 611, 714, 763] [59, 159, 303, 435, 473, 612, 715, 764] [60, 160, 304, 327, 474, 613, 716, 765] [61, 161, 305, 328, 475, 614, 717, 766] [62, 162, 306, 329, 476, 615, 718, 767] [63, 163, 307, 330, 477, 616, 719, 768] [64, 164, 308, 331, 478, 617, 720, 769] [65, 165, 309, 332, 479, 618, 721, 770] [66, 166, 310, 333, 480, 619, 722, 771] [67, 167, 311, 334, 481, 620, 723, 772] [68, 168, 312, 335, 482, 621, 724, 773] [69, 169, 313, 336, 483, 622, 725, 774] [70, 170, 314, 337, 484, 623, 726, 775] [71, 171, 315, 338, 485, 624, 727, 776] [72, 172, 316, 339, 486, 625, 728, 777] [73, 173, 317, 340, 487, 626, 729, 778] [74, 174, 318, 341, 488, 627, 730, 779] [75, 175, 319, 342, 489, 628, 731, 780] [76, 176, 320, 343, 490, 629, 732, 781] [77, 177, 321, 344, 491, 630, 733, 782] [78, 178, 322, 345, 492, 631, 734, 783] [79, 179, 323, 346, 493, 632, 735, 784] [80, 180, 324, 347, 494, 633, 736, 785] [81, 181, 325, 348, 495, 634, 737, 786] [82, 182, 326, 349, 496, 635, 738, 787] [83, 183, 218, 350, 497, 636, 739, 788] [84, 184, 219, 351, 498, 637, 740, 789] [85, 185, 220, 352, 499, 638, 741, 790] [86, 186, 221, 353, 500, 639, 742, 791] [87, 187, 222, 354, 501, 640, 743, 792] [88, 188, 223, 355, 502, 641, 744, 793] [89, 189, 224, 356, 503, 642, 745, 794] [90, 190, 225, 357, 504, 643, 746, 795] [91, 191, 226, 358, 505, 644, 747, 796] [92, 192, 227, 359, 506, 645, 748, 797] [93, 193, 228, 360, 507, 646, 749, 798] [94, 194, 229, 361, 508, 647, 750, 799] [95, 195, 230, 362, 509, 648, 751, 800] [96, 196, 231, 363, 510, 649, 752, 801] [97, 197, 232, 364, 511, 650, 753, 802] [98, 198, 233, 365, 512, 651, 754, 803] [99, 199, 234, 366, 513, 652, 755, 804] [100, 200, 235, 367, 514, 653, 756, 805] [101, 201, 236, 368, 515, 545, 757, 806] [102, 202, 237, 369, 516, 546, 758, 807] [103, 203, 238, 370, 517, 547, 759, 808] [104, 204, 239, 371, 518, 548, 760, 809] [105, 205, 240, 372, 519, 549, 761, 810] [106, 206, 241, 373, 520, 550, 762, 811] [107, 207, 242, 374, 521, 551, 654, 812] [108, 208, 243, 375, 522, 552, 655, 813] [0, 209, 244, 376, 523, 553, 656, 814] [1, 210, 245, 377, 524, 554, 657, 815] [2, 211, 246, 378, 525, 555, 658, 816] [3, 212, 247, 379, 526, 556, 659, 817] [4, 213, 248, 380, 527, 557, 660, 818] [5, 214, 249, 381, 528, 558, 661, 819] [6, 215, 250, 382, 529, 559, 662, 820] [7, 216, 251, 383, 530, 560, 663, 821] [8, 217, 252, 384, 531, 561, 664, 822] [9, 109, 253, 385, 532, 562, 665, 823] [10, 110, 254, 386, 533, 563, 666, 824] [11, 111, 255, 387, 534, 564, 667, 825] [12, 112, 256, 388, 535, 565, 668, 826] [13, 113, 257, 389, 536, 566, 669, 827] [14, 114, 258, 390, 537, 567, 670, 828] [15, 115, 259, 391, 538, 568, 671, 829] [16, 116, 260, 392, 539, 569, 672, 830] [17, 117, 261, 393, 540, 570, 673, 831] [18, 118, 262, 394, 541, 571, 674, 832] [19, 119, 263, 395, 542, 572, 675, 833] [20, 120, 264, 396, 543, 573, 676, 834] [21, 121, 265, 397, 544, 574, 677, 835] [22, 122, 266, 398, 436, 575, 678, 836] [23, 123, 267, 399, 437, 576, 679, 837] [24, 124, 268, 400, 438, 577, 680, 838] [25, 125, 269, 401, 439, 578, 681, 839] [26, 126, 270, 402, 440, 579, 682, 840] [27, 127, 271, 403, 441, 580, 683, 841] [28, 128, 272, 404, 442, 581, 684, 842] [29, 129, 273, 405, 443, 582, 685, 843] [30, 130, 274, 406, 444, 583, 686, 844] [31, 131, 275, 407, 445, 584, 687, 845] [32, 132, 276, 408, 446, 585, 688, 846] [33, 133, 277, 409, 447, 586, 689, 847] [34, 134, 278, 410, 448, 587, 690, 848] [35, 135, 279, 411, 449, 588, 691, 849] [36, 136, 280, 412, 450, 589, 692, 850] [37, 137, 281, 413, 451, 590, 693, 851] [38, 138, 282, 414, 452, 591, 694, 852] [39, 139, 283, 415, 453, 592, 695, 853] [40, 140, 284, 416, 454, 593, 696, 854] [41, 141, 285, 417, 455, 594, 697, 855] [42, 142, 286, 418, 456, 595, 698, 856] [43, 143, 287, 419, 457, 596, 699, 857] [44, 144, 288, 420, 458, 597, 700, 858] [45, 145, 289, 421, 459, 598, 701, 859] [46, 146, 290, 422, 460, 599, 702, 860] [47, 147, 291, 423, 461, 600, 703, 861] [48, 148, 292, 424, 462, 601, 704, 862] [49, 149, 293, 425, 463, 602, 705, 863] [50, 150, 294, 426, 464, 603, 706, 864] [82, 181, 296, 371, 480, 549, 692, 785] [83, 182, 297, 372, 481, 550, 693, 786] [84, 183, 298, 373, 482, 551, 694, 787] [85, 184, 299, 374, 483, 552, 695, 788] [86, 185, 300, 375, 484, 553, 696, 789] [87, 186, 301, 376, 485, 554, 697, 790] [88, 187, 302, 377, 486, 555, 698, 791] [89, 188, 303, 378, 487, 556, 699, 792] [90, 189, 304, 379, 488, 557, 700, 793] [91, 190, 305, 380, 489, 558, 701, 794] [92, 191, 306, 381, 490, 559, 702, 795] [93, 192, 307, 382, 491, 560, 703, 796] [94, 193, 308, 383, 492, 561, 704, 797] [95, 194, 309, 384, 493, 562, 705, 798] [96, 195, 310, 385, 494, 563, 706, 799] [97, 196, 311, 386, 495, 564, 707, 800] [98, 197, 312, 387, 496, 565, 708, 801] [99, 198, 313, 388, 497, 566, 709, 802] [100, 199, 314, 389, 498, 567, 710, 803] [101, 200, 315, 390, 499, 568, 711, 804] [102, 201, 316, 391, 500, 569, 712, 805] [103, 202, 317, 392, 501, 570, 713, 806] [104, 203, 318, 393, 502, 571, 714, 807] [105, 204, 319, 394, 503, 572, 715, 808] [106, 205, 320, 395, 504, 573, 716, 809] [107, 206, 321, 396, 505, 574, 717, 810] [108, 207, 322, 397, 506, 575, 718, 811] [0, 208, 323, 398, 507, 576, 719, 812] [1, 209, 324, 399, 508, 577, 720, 813] [2, 210, 325, 400, 509, 578, 721, 814] [3, 211, 326, 401, 510, 579, 722, 815] [4, 212, 218, 402, 511, 580, 723, 816] [5, 213, 219, 403, 512, 581, 724, 817] [6, 214, 220, 404, 513, 582, 725, 818] [7, 215, 221, 405, 514, 583, 726, 819] [8, 216, 222, 406, 515, 584, 727, 820] [9, 217, 223, 407, 516, 585, 728, 821] [10, 109, 224, 408, 517, 586, 729, 822] [11, 110, 225, 409, 518, 587, 730, 823] [12, 111, 226, 410, 519, 588, 731, 824] [13, 112, 227, 411, 520, 589, 732, 825] [14, 113, 228, 412, 521, 590, 733, 826] [15, 114, 229, 413, 522, 591, 734, 827] [16, 115, 230, 414, 523, 592, 735, 828] [17, 116, 231, 415, 524, 593, 736, 829] [18, 117, 232, 416, 525, 594, 737, 830] [19, 118, 233, 417, 526, 595, 738, 831] [20, 119, 234, 418, 527, 596, 739, 832] [21, 120, 235, 419, 528, 597, 740, 833] [22, 121, 236, 420, 529, 598, 741, 834] [23, 122, 237, 421, 530, 599, 742, 835] [24, 123, 238, 422, 531, 600, 743, 836] [25, 124, 239, 423, 532, 601, 744, 837] [26, 125, 240, 424, 533, 602, 745, 838] [27, 126, 241, 425, 534, 603, 746, 839] [28, 127, 242, 426, 535, 604, 747, 840] [29, 128, 243, 427, 536, 605, 748, 841] [30, 129, 244, 428, 537, 606, 749, 842] [31, 130, 245, 429, 538, 607, 750, 843] [32, 131, 246, 430, 539, 608, 751, 844] [33, 132, 247, 431, 540, 609, 752, 845] [34, 133, 248, 432, 541, 610, 753, 846] [35, 134, 249, 433, 542, 611, 754, 847] [36, 135, 250, 434, 543, 612, 755, 848] [37, 136, 251, 435, 544, 613, 756, 849] [38, 137, 252, 327, 436, 614, 757, 850] [39, 138, 253, 328, 437, 615, 758, 851] [40, 139, 254, 329, 438, 616, 759, 852] [41, 140, 255, 330, 439, 617, 760, 853] [42, 141, 256, 331, 440, 618, 761, 854] [43, 142, 257, 332, 441, 619, 762, 855] [44, 143, 258, 333, 442, 620, 654, 856] [45, 144, 259, 334, 443, 621, 655, 857] [46, 145, 260, 335, 444, 622, 656, 858] [47, 146, 261, 336, 445, 623, 657, 859] [48, 147, 262, 337, 446, 624, 658, 860] [49, 148, 263, 338, 447, 625, 659, 861] [50, 149, 264, 339, 448, 626, 660, 862] [51, 150, 265, 340, 449, 627, 661, 863] [52, 151, 266, 341, 450, 628, 662, 864] [53, 152, 267, 342, 451, 629, 663, 865] [54, 153, 268, 343, 452, 630, 664, 866] [55, 154, 269, 344, 453, 631, 665, 867] [56, 155, 270, 345, 454, 632, 666, 868] [57, 156, 271, 346, 455, 633, 667, 869] [58, 157, 272, 347, 456, 634, 668, 870] [59, 158, 273, 348, 457, 635, 669, 871] [60, 159, 274, 349, 458, 636, 670, 763] [61, 160, 275, 350, 459, 637, 671, 764] [62, 161, 276, 351, 460, 638, 672, 765] [63, 162, 277, 352, 461, 639, 673, 766] [64, 163, 278, 353, 462, 640, 674, 767] [65, 164, 279, 354, 463, 641, 675, 768] [66, 165, 280, 355, 464, 642, 676, 769] [67, 166, 281, 356, 465, 643, 677, 770] [68, 167, 282, 357, 466, 644, 678, 771] [69, 168, 283, 358, 467, 645, 679, 772] [70, 169, 284, 359, 468, 646, 680, 773] [71, 170, 285, 360, 469, 647, 681, 774] [72, 171, 286, 361, 470, 648, 682, 775] [73, 172, 287, 362, 471, 649, 683, 776] [74, 173, 288, 363, 472, 650, 684, 777] [75, 174, 289, 364, 473, 651, 685, 778] [76, 175, 290, 365, 474, 652, 686, 779] [77, 176, 291, 366, 475, 653, 687, 780] [78, 177, 292, 367, 476, 545, 688, 781] [79, 178, 293, 368, 477, 546, 689, 782] [80, 179, 294, 369, 478, 547, 690, 783] [81, 180, 295, 370, 479, 548, 691, 784] [70, 172, 283, 409, 508, 556, 719, 807] [71, 173, 284, 410, 509, 557, 720, 808] [72, 174, 285, 411, 510, 558, 721, 809] [73, 175, 286, 412, 511, 559, 722, 810] [74, 176, 287, 413, 512, 560, 723, 811] [75, 177, 288, 414, 513, 561, 724, 812] [76, 178, 289, 415, 514, 562, 725, 813] [77, 179, 290, 416, 515, 563, 726, 814] [78, 180, 291, 417, 516, 564, 727, 815] [79, 181, 292, 418, 517, 565, 728, 816] [80, 182, 293, 419, 518, 566, 729, 817] [81, 183, 294, 420, 519, 567, 730, 818] [82, 184, 295, 421, 520, 568, 731, 819] [83, 185, 296, 422, 521, 569, 732, 820] [84, 186, 297, 423, 522, 570, 733, 821] [85, 187, 298, 424, 523, 571, 734, 822] [86, 188, 299, 425, 524, 572, 735, 823] [87, 189, 300, 426, 525, 573, 736, 824] [88, 190, 301, 427, 526, 574, 737, 825] [89, 191, 302, 428, 527, 575, 738, 826] [90, 192, 303, 429, 528, 576, 739, 827] [91, 193, 304, 430, 529, 577, 740, 828] [92, 194, 305, 431, 530, 578, 741, 829] [93, 195, 306, 432, 531, 579, 742, 830] [94, 196, 307, 433, 532, 580, 743, 831] [95, 197, 308, 434, 533, 581, 744, 832] [96, 198, 309, 435, 534, 582, 745, 833] [97, 199, 310, 327, 535, 583, 746, 834] [98, 200, 311, 328, 536, 584, 747, 835] [99, 201, 312, 329, 537, 585, 748, 836] [100, 202, 313, 330, 538, 586, 749, 837] [101, 203, 314, 331, 539, 587, 750, 838] [102, 204, 315, 332, 540, 588, 751, 839] [103, 205, 316, 333, 541, 589, 752, 840] [104, 206, 317, 334, 542, 590, 753, 841] [105, 207, 318, 335, 543, 591, 754, 842] [106, 208, 319, 336, 544, 592, 755, 843] [107, 209, 320, 337, 436, 593, 756, 844] [108, 210, 321, 338, 437, 594, 757, 845] [0, 211, 322, 339, 438, 595, 758, 846] [1, 212, 323, 340, 439, 596, 759, 847] [2, 213, 324, 341, 440, 597, 760, 848] [3, 214, 325, 342, 441, 598, 761, 849] [4, 215, 326, 343, 442, 599, 762, 850] [5, 216, 218, 344, 443, 600, 654, 851] [6, 217, 219, 345, 444, 601, 655, 852] [7, 109, 220, 346, 445, 602, 656, 853] [8, 110, 221, 347, 446, 603, 657, 854] [9, 111, 222, 348, 447, 604, 658, 855] [10, 112, 223, 349, 448, 605, 659, 856] [11, 113, 224, 350, 449, 606, 660, 857] [12, 114, 225, 351, 450, 607, 661, 858] [13, 115, 226, 352, 451, 608, 662, 859] [14, 116, 227, 353, 452, 609, 663, 860] [15, 117, 228, 354, 453, 610, 664, 861] [16, 118, 229, 355, 454, 611, 665, 862] [17, 119, 230, 356, 455, 612, 666, 863] [18, 120, 231, 357, 456, 613, 667, 864] [19, 121, 232, 358, 457, 614, 668, 865] [20, 122, 233, 359, 458, 615, 669, 866] [21, 123, 234, 360, 459, 616, 670, 867] [22, 124, 235, 361, 460, 617, 671, 868] [23, 125, 236, 362, 461, 618, 672, 869] [24, 126, 237, 363, 462, 619, 673, 870] [25, 127, 238, 364, 463, 620, 674, 871] [26, 128, 239, 365, 464, 621, 675, 763] [27, 129, 240, 366, 465, 622, 676, 764] [28, 130, 241, 367, 466, 623, 677, 765] [29, 131, 242, 368, 467, 624, 678, 766] [30, 132, 243, 369, 468, 625, 679, 767] [31, 133, 244, 370, 469, 626, 680, 768] [32, 134, 245, 371, 470, 627, 681, 769] [33, 135, 246, 372, 471, 628, 682, 770] [34, 136, 247, 373, 472, 629, 683, 771] [35, 137, 248, 374, 473, 630, 684, 772] [36, 138, 249, 375, 474, 631, 685, 773] [37, 139, 250, 376, 475, 632, 686, 774] [38, 140, 251, 377, 476, 633, 687, 775] [39, 141, 252, 378, 477, 634, 688, 776] [40, 142, 253, 379, 478, 635, 689, 777] [41, 143, 254, 380, 479, 636, 690, 778] [42, 144, 255, 381, 480, 637, 691, 779] [43, 145, 256, 382, 481, 638, 692, 780] [44, 146, 257, 383, 482, 639, 693, 781] [45, 147, 258, 384, 483, 640, 694, 782] [46, 148, 259, 385, 484, 641, 695, 783] [47, 149, 260, 386, 485, 642, 696, 784] [48, 150, 261, 387, 486, 643, 697, 785] [49, 151, 262, 388, 487, 644, 698, 786] [50, 152, 263, 389, 488, 645, 699, 787] [51, 153, 264, 390, 489, 646, 700, 788] [52, 154, 265, 391, 490, 647, 701, 789] [53, 155, 266, 392, 491, 648, 702, 790] [54, 156, 267, 393, 492, 649, 703, 791] [55, 157, 268, 394, 493, 650, 704, 792] [56, 158, 269, 395, 494, 651, 705, 793] [57, 159, 270, 396, 495, 652, 706, 794] [58, 160, 271, 397, 496, 653, 707, 795] [59, 161, 272, 398, 497, 545, 708, 796] [60, 162, 273, 399, 498, 546, 709, 797] [61, 163, 274, 400, 499, 547, 710, 798] [62, 164, 275, 401, 500, 548, 711, 799] [63, 165, 276, 402, 501, 549, 712, 800] [64, 166, 277, 403, 502, 550, 713, 801] [65, 167, 278, 404, 503, 551, 714, 802] [66, 168, 279, 405, 504, 552, 715, 803] [67, 169, 280, 406, 505, 553, 716, 804] [68, 170, 281, 407, 506, 554, 717, 805] [69, 171, 282, 408, 507, 555, 718, 806]
H_Z (327 checks, sparse supports)
[14, 112, 227, 428, 537, 605, 748, 826] [15, 113, 228, 429, 538, 606, 749, 827] [16, 114, 229, 430, 539, 607, 750, 828] [17, 115, 230, 431, 540, 608, 751, 829] [18, 116, 231, 432, 541, 609, 752, 830] [19, 117, 232, 433, 542, 610, 753, 831] [20, 118, 233, 434, 543, 611, 754, 832] [21, 119, 234, 435, 544, 612, 755, 833] [22, 120, 235, 327, 436, 613, 756, 834] [23, 121, 236, 328, 437, 614, 757, 835] [24, 122, 237, 329, 438, 615, 758, 836] [25, 123, 238, 330, 439, 616, 759, 837] [26, 124, 239, 331, 440, 617, 760, 838] [27, 125, 240, 332, 441, 618, 761, 839] [28, 126, 241, 333, 442, 619, 762, 840] [29, 127, 242, 334, 443, 620, 654, 841] [30, 128, 243, 335, 444, 621, 655, 842] [31, 129, 244, 336, 445, 622, 656, 843] [32, 130, 245, 337, 446, 623, 657, 844] [33, 131, 246, 338, 447, 624, 658, 845] [34, 132, 247, 339, 448, 625, 659, 846] [35, 133, 248, 340, 449, 626, 660, 847] [36, 134, 249, 341, 450, 627, 661, 848] [37, 135, 250, 342, 451, 628, 662, 849] [38, 136, 251, 343, 452, 629, 663, 850] [39, 137, 252, 344, 453, 630, 664, 851] [40, 138, 253, 345, 454, 631, 665, 852] [41, 139, 254, 346, 455, 632, 666, 853] [42, 140, 255, 347, 456, 633, 667, 854] [43, 141, 256, 348, 457, 634, 668, 855] [44, 142, 257, 349, 458, 635, 669, 856] [45, 143, 258, 350, 459, 636, 670, 857] [46, 144, 259, 351, 460, 637, 671, 858] [47, 145, 260, 352, 461, 638, 672, 859] [48, 146, 261, 353, 462, 639, 673, 860] [49, 147, 262, 354, 463, 640, 674, 861] [50, 148, 263, 355, 464, 641, 675, 862] [51, 149, 264, 356, 465, 642, 676, 863] [52, 150, 265, 357, 466, 643, 677, 864] [53, 151, 266, 358, 467, 644, 678, 865] [54, 152, 267, 359, 468, 645, 679, 866] [55, 153, 268, 360, 469, 646, 680, 867] [56, 154, 269, 361, 470, 647, 681, 868] [57, 155, 270, 362, 471, 648, 682, 869] [58, 156, 271, 363, 472, 649, 683, 870] [59, 157, 272, 364, 473, 650, 684, 871] [60, 158, 273, 365, 474, 651, 685, 763] [61, 159, 274, 366, 475, 652, 686, 764] [62, 160, 275, 367, 476, 653, 687, 765] [63, 161, 276, 368, 477, 545, 688, 766] [64, 162, 277, 369, 478, 546, 689, 767] [65, 163, 278, 370, 479, 547, 690, 768] [66, 164, 279, 371, 480, 548, 691, 769] [67, 165, 280, 372, 481, 549, 692, 770] [68, 166, 281, 373, 482, 550, 693, 771] [69, 167, 282, 374, 483, 551, 694, 772] [70, 168, 283, 375, 484, 552, 695, 773] [71, 169, 284, 376, 485, 553, 696, 774] [72, 170, 285, 377, 486, 554, 697, 775] [73, 171, 286, 378, 487, 555, 698, 776] [74, 172, 287, 379, 488, 556, 699, 777] [75, 173, 288, 380, 489, 557, 700, 778] [76, 174, 289, 381, 490, 558, 701, 779] [77, 175, 290, 382, 491, 559, 702, 780] [78, 176, 291, 383, 492, 560, 703, 781] [79, 177, 292, 384, 493, 561, 704, 782] [80, 178, 293, 385, 494, 562, 705, 783] [81, 179, 294, 386, 495, 563, 706, 784] [82, 180, 295, 387, 496, 564, 707, 785] [83, 181, 296, 388, 497, 565, 708, 786] [84, 182, 297, 389, 498, 566, 709, 787] [85, 183, 298, 390, 499, 567, 710, 788] [86, 184, 299, 391, 500, 568, 711, 789] [87, 185, 300, 392, 501, 569, 712, 790] [88, 186, 301, 393, 502, 570, 713, 791] [89, 187, 302, 394, 503, 571, 714, 792] [90, 188, 303, 395, 504, 572, 715, 793] [91, 189, 304, 396, 505, 573, 716, 794] [92, 190, 305, 397, 506, 574, 717, 795] [93, 191, 306, 398, 507, 575, 718, 796] [94, 192, 307, 399, 508, 576, 719, 797] [95, 193, 308, 400, 509, 577, 720, 798] [96, 194, 309, 401, 510, 578, 721, 799] [97, 195, 310, 402, 511, 579, 722, 800] [98, 196, 311, 403, 512, 580, 723, 801] [99, 197, 312, 404, 513, 581, 724, 802] [100, 198, 313, 405, 514, 582, 725, 803] [101, 199, 314, 406, 515, 583, 726, 804] [102, 200, 315, 407, 516, 584, 727, 805] [103, 201, 316, 408, 517, 585, 728, 806] [104, 202, 317, 409, 518, 586, 729, 807] [105, 203, 318, 410, 519, 587, 730, 808] [106, 204, 319, 411, 520, 588, 731, 809] [107, 205, 320, 412, 521, 589, 732, 810] [108, 206, 321, 413, 522, 590, 733, 811] [0, 207, 322, 414, 523, 591, 734, 812] [1, 208, 323, 415, 524, 592, 735, 813] [2, 209, 324, 416, 525, 593, 736, 814] [3, 210, 325, 417, 526, 594, 737, 815] [4, 211, 326, 418, 527, 595, 738, 816] [5, 212, 218, 419, 528, 596, 739, 817] [6, 213, 219, 420, 529, 597, 740, 818] [7, 214, 220, 421, 530, 598, 741, 819] [8, 215, 221, 422, 531, 599, 742, 820] [9, 216, 222, 423, 532, 600, 743, 821] [10, 217, 223, 424, 533, 601, 744, 822] [11, 109, 224, 425, 534, 602, 745, 823] [12, 110, 225, 426, 535, 603, 746, 824] [13, 111, 226, 427, 536, 604, 747, 825] [10, 143, 254, 418, 517, 596, 759, 856] [11, 144, 255, 419, 518, 597, 760, 857] [12, 145, 256, 420, 519, 598, 761, 858] [13, 146, 257, 421, 520, 599, 762, 859] [14, 147, 258, 422, 521, 600, 654, 860] [15, 148, 259, 423, 522, 601, 655, 861] [16, 149, 260, 424, 523, 602, 656, 862] [17, 150, 261, 425, 524, 603, 657, 863] [18, 151, 262, 426, 525, 604, 658, 864] [19, 152, 263, 427, 526, 605, 659, 865] [20, 153, 264, 428, 527, 606, 660, 866] [21, 154, 265, 429, 528, 607, 661, 867] [22, 155, 266, 430, 529, 608, 662, 868] [23, 156, 267, 431, 530, 609, 663, 869] [24, 157, 268, 432, 531, 610, 664, 870] [25, 158, 269, 433, 532, 611, 665, 871] [26, 159, 270, 434, 533, 612, 666, 763] [27, 160, 271, 435, 534, 613, 667, 764] [28, 161, 272, 327, 535, 614, 668, 765] [29, 162, 273, 328, 536, 615, 669, 766] [30, 163, 274, 329, 537, 616, 670, 767] [31, 164, 275, 330, 538, 617, 671, 768] [32, 165, 276, 331, 539, 618, 672, 769] [33, 166, 277, 332, 540, 619, 673, 770] [34, 167, 278, 333, 541, 620, 674, 771] [35, 168, 279, 334, 542, 621, 675, 772] [36, 169, 280, 335, 543, 622, 676, 773] [37, 170, 281, 336, 544, 623, 677, 774] [38, 171, 282, 337, 436, 624, 678, 775] [39, 172, 283, 338, 437, 625, 679, 776] [40, 173, 284, 339, 438, 626, 680, 777] [41, 174, 285, 340, 439, 627, 681, 778] [42, 175, 286, 341, 440, 628, 682, 779] [43, 176, 287, 342, 441, 629, 683, 780] [44, 177, 288, 343, 442, 630, 684, 781] [45, 178, 289, 344, 443, 631, 685, 782] [46, 179, 290, 345, 444, 632, 686, 783] [47, 180, 291, 346, 445, 633, 687, 784] [48, 181, 292, 347, 446, 634, 688, 785] [49, 182, 293, 348, 447, 635, 689, 786] [50, 183, 294, 349, 448, 636, 690, 787] [51, 184, 295, 350, 449, 637, 691, 788] [52, 185, 296, 351, 450, 638, 692, 789] [53, 186, 297, 352, 451, 639, 693, 790] [54, 187, 298, 353, 452, 640, 694, 791] [55, 188, 299, 354, 453, 641, 695, 792] [56, 189, 300, 355, 454, 642, 696, 793] [57, 190, 301, 356, 455, 643, 697, 794] [58, 191, 302, 357, 456, 644, 698, 795] [59, 192, 303, 358, 457, 645, 699, 796] [60, 193, 304, 359, 458, 646, 700, 797] [61, 194, 305, 360, 459, 647, 701, 798] [62, 195, 306, 361, 460, 648, 702, 799] [63, 196, 307, 362, 461, 649, 703, 800] [64, 197, 308, 363, 462, 650, 704, 801] [65, 198, 309, 364, 463, 651, 705, 802] [66, 199, 310, 365, 464, 652, 706, 803] [67, 200, 311, 366, 465, 653, 707, 804] [68, 201, 312, 367, 466, 545, 708, 805] [69, 202, 313, 368, 467, 546, 709, 806] [70, 203, 314, 369, 468, 547, 710, 807] [71, 204, 315, 370, 469, 548, 711, 808] [72, 205, 316, 371, 470, 549, 712, 809] [73, 206, 317, 372, 471, 550, 713, 810] [74, 207, 318, 373, 472, 551, 714, 811] [75, 208, 319, 374, 473, 552, 715, 812] [76, 209, 320, 375, 474, 553, 716, 813] [77, 210, 321, 376, 475, 554, 717, 814] [78, 211, 322, 377, 476, 555, 718, 815] [79, 212, 323, 378, 477, 556, 719, 816] [80, 213, 324, 379, 478, 557, 720, 817] [81, 214, 325, 380, 479, 558, 721, 818] [82, 215, 326, 381, 480, 559, 722, 819] [83, 216, 218, 382, 481, 560, 723, 820] [84, 217, 219, 383, 482, 561, 724, 821] [85, 109, 220, 384, 483, 562, 725, 822] [86, 110, 221, 385, 484, 563, 726, 823] [87, 111, 222, 386, 485, 564, 727, 824] [88, 112, 223, 387, 486, 565, 728, 825] [89, 113, 224, 388, 487, 566, 729, 826] [90, 114, 225, 389, 488, 567, 730, 827] [91, 115, 226, 390, 489, 568, 731, 828] [92, 116, 227, 391, 490, 569, 732, 829] [93, 117, 228, 392, 491, 570, 733, 830] [94, 118, 229, 393, 492, 571, 734, 831] [95, 119, 230, 394, 493, 572, 735, 832] [96, 120, 231, 395, 494, 573, 736, 833] [97, 121, 232, 396, 495, 574, 737, 834] [98, 122, 233, 397, 496, 575, 738, 835] [99, 123, 234, 398, 497, 576, 739, 836] [100, 124, 235, 399, 498, 577, 740, 837] [101, 125, 236, 400, 499, 578, 741, 838] [102, 126, 237, 401, 500, 579, 742, 839] [103, 127, 238, 402, 501, 580, 743, 840] [104, 128, 239, 403, 502, 581, 744, 841] [105, 129, 240, 404, 503, 582, 745, 842] [106, 130, 241, 405, 504, 583, 746, 843] [107, 131, 242, 406, 505, 584, 747, 844] [108, 132, 243, 407, 506, 585, 748, 845] [0, 133, 244, 408, 507, 586, 749, 846] [1, 134, 245, 409, 508, 587, 750, 847] [2, 135, 246, 410, 509, 588, 751, 848] [3, 136, 247, 411, 510, 589, 752, 849] [4, 137, 248, 412, 511, 590, 753, 850] [5, 138, 249, 413, 512, 591, 754, 851] [6, 139, 250, 414, 513, 592, 755, 852] [7, 140, 251, 415, 514, 593, 756, 853] [8, 141, 252, 416, 515, 594, 757, 854] [9, 142, 253, 417, 516, 595, 758, 855] [72, 142, 286, 363, 510, 619, 722, 777] [73, 143, 287, 364, 511, 620, 723, 778] [74, 144, 288, 365, 512, 621, 724, 779] [75, 145, 289, 366, 513, 622, 725, 780] [76, 146, 290, 367, 514, 623, 726, 781] [77, 147, 291, 368, 515, 624, 727, 782] [78, 148, 292, 369, 516, 625, 728, 783] [79, 149, 293, 370, 517, 626, 729, 784] [80, 150, 294, 371, 518, 627, 730, 785] [81, 151, 295, 372, 519, 628, 731, 786] [82, 152, 296, 373, 520, 629, 732, 787] [83, 153, 297, 374, 521, 630, 733, 788] [84, 154, 298, 375, 522, 631, 734, 789] [85, 155, 299, 376, 523, 632, 735, 790] [86, 156, 300, 377, 524, 633, 736, 791] [87, 157, 301, 378, 525, 634, 737, 792] [88, 158, 302, 379, 526, 635, 738, 793] [89, 159, 303, 380, 527, 636, 739, 794] [90, 160, 304, 381, 528, 637, 740, 795] [91, 161, 305, 382, 529, 638, 741, 796] [92, 162, 306, 383, 530, 639, 742, 797] [93, 163, 307, 384, 531, 640, 743, 798] [94, 164, 308, 385, 532, 641, 744, 799] [95, 165, 309, 386, 533, 642, 745, 800] [96, 166, 310, 387, 534, 643, 746, 801] [97, 167, 311, 388, 535, 644, 747, 802] [98, 168, 312, 389, 536, 645, 748, 803] [99, 169, 313, 390, 537, 646, 749, 804] [100, 170, 314, 391, 538, 647, 750, 805] [101, 171, 315, 392, 539, 648, 751, 806] [102, 172, 316, 393, 540, 649, 752, 807] [103, 173, 317, 394, 541, 650, 753, 808] [104, 174, 318, 395, 542, 651, 754, 809] [105, 175, 319, 396, 543, 652, 755, 810] [106, 176, 320, 397, 544, 653, 756, 811] [107, 177, 321, 398, 436, 545, 757, 812] [108, 178, 322, 399, 437, 546, 758, 813] [0, 179, 323, 400, 438, 547, 759, 814] [1, 180, 324, 401, 439, 548, 760, 815] [2, 181, 325, 402, 440, 549, 761, 816] [3, 182, 326, 403, 441, 550, 762, 817] [4, 183, 218, 404, 442, 551, 654, 818] [5, 184, 219, 405, 443, 552, 655, 819] [6, 185, 220, 406, 444, 553, 656, 820] [7, 186, 221, 407, 445, 554, 657, 821] [8, 187, 222, 408, 446, 555, 658, 822] [9, 188, 223, 409, 447, 556, 659, 823] [10, 189, 224, 410, 448, 557, 660, 824] [11, 190, 225, 411, 449, 558, 661, 825] [12, 191, 226, 412, 450, 559, 662, 826] [13, 192, 227, 413, 451, 560, 663, 827] [14, 193, 228, 414, 452, 561, 664, 828] [15, 194, 229, 415, 453, 562, 665, 829] [16, 195, 230, 416, 454, 563, 666, 830] [17, 196, 231, 417, 455, 564, 667, 831] [18, 197, 232, 418, 456, 565, 668, 832] [19, 198, 233, 419, 457, 566, 669, 833] [20, 199, 234, 420, 458, 567, 670, 834] [21, 200, 235, 421, 459, 568, 671, 835] [22, 201, 236, 422, 460, 569, 672, 836] [23, 202, 237, 423, 461, 570, 673, 837] [24, 203, 238, 424, 462, 571, 674, 838] [25, 204, 239, 425, 463, 572, 675, 839] [26, 205, 240, 426, 464, 573, 676, 840] [27, 206, 241, 427, 465, 574, 677, 841] [28, 207, 242, 428, 466, 575, 678, 842] [29, 208, 243, 429, 467, 576, 679, 843] [30, 209, 244, 430, 468, 577, 680, 844] [31, 210, 245, 431, 469, 578, 681, 845] [32, 211, 246, 432, 470, 579, 682, 846] [33, 212, 247, 433, 471, 580, 683, 847] [34, 213, 248, 434, 472, 581, 684, 848] [35, 214, 249, 435, 473, 582, 685, 849] [36, 215, 250, 327, 474, 583, 686, 850] [37, 216, 251, 328, 475, 584, 687, 851] [38, 217, 252, 329, 476, 585, 688, 852] [39, 109, 253, 330, 477, 586, 689, 853] [40, 110, 254, 331, 478, 587, 690, 854] [41, 111, 255, 332, 479, 588, 691, 855] [42, 112, 256, 333, 480, 589, 692, 856] [43, 113, 257, 334, 481, 590, 693, 857] [44, 114, 258, 335, 482, 591, 694, 858] [45, 115, 259, 336, 483, 592, 695, 859] [46, 116, 260, 337, 484, 593, 696, 860] [47, 117, 261, 338, 485, 594, 697, 861] [48, 118, 262, 339, 486, 595, 698, 862] [49, 119, 263, 340, 487, 596, 699, 863] [50, 120, 264, 341, 488, 597, 700, 864] [51, 121, 265, 342, 489, 598, 701, 865] [52, 122, 266, 343, 490, 599, 702, 866] [53, 123, 267, 344, 491, 600, 703, 867] [54, 124, 268, 345, 492, 601, 704, 868] [55, 125, 269, 346, 493, 602, 705, 869] [56, 126, 270, 347, 494, 603, 706, 870] [57, 127, 271, 348, 495, 604, 707, 871] [58, 128, 272, 349, 496, 605, 708, 763] [59, 129, 273, 350, 497, 606, 709, 764] [60, 130, 274, 351, 498, 607, 710, 765] [61, 131, 275, 352, 499, 608, 711, 766] [62, 132, 276, 353, 500, 609, 712, 767] [63, 133, 277, 354, 501, 610, 713, 768] [64, 134, 278, 355, 502, 611, 714, 769] [65, 135, 279, 356, 503, 612, 715, 770] [66, 136, 280, 357, 504, 613, 716, 771] [67, 137, 281, 358, 505, 614, 717, 772] [68, 138, 282, 359, 506, 615, 718, 773] [69, 139, 283, 360, 507, 616, 719, 774] [70, 140, 284, 361, 508, 617, 720, 775] [71, 141, 285, 362, 509, 618, 721, 776]
Code ID 872-222-18 · download JSON · raw on GitHub